A study of generalized Hubbard model in the paramagnetic phase by means of the COM is reported in Refs. [97,98]. In particular the following properties have been computed:
Particular attention has been paid to the role played by the intersite interaction which drives important changes in the electronic properties of the system. Using a fully self-consistent treatment we have obtained both the local and the single-particle properties of the model . The former show a tendency towards a charge ordered phase instability. The latter are modified quantitatively, but not qualitatively, with respect to the results obtained with the usual Hubbard Hamiltonian. This could permit to fit more accurately the experimental data for the cuprates superconductors. The value of the filling at which the Fermi level crosses the van Hove singularity in the density of states has been studied as a function of the coupling constants. A comparison with the experimental data for the magnetic and thermodynamical properties of the high-T superconductors suggests an intermediate regime for the on-site coupling and a weak regime for the intersite one as the most adequate to describe these materials. We have also considered a generalization of the original Hubbard model where correlated hopping and intersite repulsion are considered simultaneously . In this framework, we have obtained a reasonable set of parameters that fit, as regards , both the volume of the Fermi surface and the doping at which the van Hove singularity crosses the Fermi level producing a strong enhancement of the entropy and the uniform static spin magnetic susceptibility.